The Fefferman-Stein-Type Inequality for the Kakeya Maximal Operator Ⅱ

作     者：Hitoshi TANAKA 

作者机构：Department of Mathematics Gakushuin University 1-5-1 Mejiro Toshima-ku Tokyo 171-8588 Japan 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2002年第18卷第3期

页      面：447-454页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by Japan Society for the Promotion of Sciences and Fujukai Foundation 

主　　题：Maximal functions Weighted inequalties 

摘      要：Let K, 0 ±1, be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricity . The (so-called) Fefferman-Stein-type inequality: $|| {K_\delta f} ||_{L^d({{\rm R}^d,w})} \le C_d ({1 \over \delta})^{(d - 2)/2d}(\log ({1 \over \delta } ))^{\alpha_d} || f ||_{L^d ({\rm R}^d,K_{\delta}w})}$is shown, where Cd and d are constants depending only on the dimension d and w is a weight. The result contains the exponent (d-2)/2d which is smaller than the exponent (d-2)(d-1)/d(2d-3) obtained in [7].